Is there any difference between the convolution operation applied to images and applied to other numerical 2D data?
Short answer is no. You can't use a model trained for one task to predict on a totally different task. Even if the second task was another image classification task, the CNN would have to be fine tuned for the new data to work.

A couple of things to note...

1) CNNs are good for images due to their nature. It isn't necessary that they'd be good for any 2-dimensional input.  

2) By 2D numerical data I'm assuming you don't mean tabular data.